Divide the following complex numbers: $\dfrac{3 e^{19\pi i / 12}}{ e^{4\pi i / 3}}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Answer: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $3 e^{19\pi i / 12}$ ) has angle $\frac{19}{12}\pi$ and radius 3. The second number ( $ e^{4\pi i / 3}$ ) has angle $\frac{4}{3}\pi$ and radius 1. The radius of the result will be $\frac{3}{1}$ , which is 3. The angle of the result is $\frac{19}{12}\pi - \frac{4}{3}\pi = \frac{1}{4}\pi$ The radius of the result is $3$ and the angle of the result is $\frac{1}{4}\pi$.